Joint Canonical Decomposition of Sixth Order Cumulants: Application to Blind Underdetermined Mixture Identification

Cumulant-based methods were proposed to blindly identify underdetermined mixtures of P statistically independent narrowband sources received by an array of N sensors. These methods exploit the algebraic structure of q- th (q isin {2,4,6}) order cumulant arrays as a function of the mixture. Although these algorithms give good results in operational contexts, they cannot process more than N² sources from N sensors. We propose in this paper three new blind mixture identification methods based on a joint canonical decomposition of several sixth order cumulant arrays. An identifiability study and computer simulations show that these three algorithms can process more sources than the classical cumulant-based approaches.